Budapest -> Seville

You can get a rough idea of transit times at rome2rio.com. With the exception of flying, all the options require at least 24 hours. Trains look expensive, but I didn't check a rail website for precise information. The bus goes by way of Romania (interesting country, but certainly not on the direct route).

I'm a huge fan of trains and buses within Europe, but in this case I'd be flying. Not necessarily into Seville, just into a place they'd like to see from which Seville wouldn't be too long a journey. So, maybe Barcelona, Madrid, or Lisbon.

Now, if they will have finished what they want to see in Budapest by May 21 or 22 and don't want to spend time in Seville before May 28 (since one daughter will be staying there), it wouldn't be totally crazy to travel by train, breaking the journey in a couple of places along the way. They'd just need to be careful about the last stop-over since timely arrival in Seville is important. It looks (from rome2rio.com) as if that would be a costly week, however.

I am confused as to when you and the daughter that must be in Seville on the 28th arrive in Budapest?

Do they want to go directly to Seville ? If not these are all good options.

Paris, 2h15m. Rome, 1H40m Barcelona 2h30m. All have flights to Seville.

For budget carriers, look at
Vueling and Transavia France.

Adding to the confusion, the same question with responses is running the Spain section.